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<b>let </b><font color="Maroon" title="c1">G</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="lattices.html#V4" title="LATTICES:attr.4">join-commutative</a> <a href="lattices.html#V5" title="LATTICES:attr.5">join-associative</a> <a href="robbins1.html#V4" title="ROBBINS1:attr.4">Robbins</a>  <a href="robbins1.html#L2" title="ROBBINS1:struct.2">ComplLattStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( for <font color="Olive" title="b1">z</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> holds   <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Olive" title="b1">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">z</font> ) implies <font color="Maroon" title="c1">G</font> is <a href="robbins1.html#V5" title="ROBBINS1:attr.5">Huntington</a> )</span><br/>

<b>assume </b><a NAME="E1:95"/><i><font color="Green" title="E55">A1</font></i>: 
for <font color="Olive" title="b1">z</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> holds   <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Olive" title="b1">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">z</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">G</font> is <a href="robbins1.html#V5" title="ROBBINS1:attr.5">Huntington</a></span><br/>

<b>let </b><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="robbins1.html#D12" target="_self" title="ROBBINS1:def.12">ROBBINS1:def 12</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> holds  <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Olive" title="b1">y</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Olive" title="b1">y</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font></span><br/><b>let </b><font color="Maroon" title="c3">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c3">y</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c3">y</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">y</font></span><br/>



<a NAME="E2:95"/><i><font color="Green" title="E56">A2</font></i>: 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c3">y</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c3">y</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c3">y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></i>;<br/>
<span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c3">y</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c3">y</font></span>)</span></span>)</span></span>)</span> = 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c3">y</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c3">y</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="robbins1.html#E1:95"><i><font color="Green" title="E55">A1</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c3">y</font>
<b>by </b><i><a class="txt" href="robbins1.html#E1:95"><i><font color="Green" title="E55">A1</font></i></a>, <a class="txt" href="robbins1.html#E2:95"><i><font color="Green" title="E56">A2</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E4:95"/>
<span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c3">y</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c3">y</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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